Page:Newton's Principia (1846).djvu/418

 the excesses of the length of the pendulum at Paris above the lengths of the isochronal pendulums observed in those latitudes are a little greater than by the table of the lengths of the pendulum before computed. And therefore the earth is a little higher under the equator than by the preceding calculus, and a little denser at the centre than in mines near the su face, unless, perhaps, the heats of the torrid zone have a little extended the length of the pendulums.

For M. Picart has observed, that a rod of iron, which in frosty weather in the winter season was one foot long, when heated by lire, was lengthened into one foot and ¼ line. Afterward M. de la Hire found that a rod of iron, which in the like winter season was 6 feet long, when exposed to the heat of the summer sun, was extended into 6 feet and ⅔ line. In the former case the heat was greater than in the latter; but in the latter it was greater than the heat of the external parts of a human body; for metals exposed to the summer sun acquire a very considerable degree of heat. But the rod of a pendulum clock is never exposed to the heat of the summer sun, nor ever acquires a heat equal to that of the external parts of a human body; and, therefore, though the 3 feet rod of a pendulum clock will indeed be a little longer in the summer than in the winter season, yet the difference will scarcely amount to ¼ line. Therefore the total difference of the lengths of isochronal pendulums in different climates cannot be ascribed to the difference of heat; nor indeed to the mistakes of the French astronomers. For although there is not a perfect agreement betwixt their observations, yet the errors are so small that they may be neglected; and in this they all agree, that isochronal pendulums are shorter under the equator than at the Royal Observatory of Paris, by a difference not less than 1¼ line, nor greater than 2⅔ lines. By the observations of M. Richer, in the island of Cayenne, the difference was 1¼ line. That difference being corrected by those of M. des Hayes, becomes 1½ line or 1¾ line. By the less accurate observations of others, the same was made about two lines. And this dis agreement might arise partly from the errors of the observations, partly from the dissimilitude of the internal parts of the earth, and the height of mountains; partly from the different heats of the air.

I take an iron rod of 3 feet long to be shorter by a sixth part of one line in winter time with us here in England than in the summer. Because of the great heats under the equator, subduct this quantity from the difference of one line and a quarter observed by M. Richer, and there will remain one line $1/12$, which agrees very well with 1$87/1000$ line collected, by the theory a little before. M. Richer repeated his observations, made in the island of Cayenne, every week for ten months together, and compared the lengths of the pendulum which he had there noted in the iron rods with the lengths thereof which he observed in France. This diligence and care seems to have been wanting to the other observers. If this gentleman's observations